Stochastic games with lexicographic reachability-safety objectives

K. Chatterjee, J.P. Katoen, M. Weininger, T. Winkler, in:, International Conference on Computer Aided Verification, Springer Nature, 2020, pp. 398–420.

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Author
Chatterjee, KrishnenduIST Austria ; Katoen, Joost PIST Austria; Weininger, Maximilian; Winkler, Tobias
Department
Series Title
LNCS
Abstract
We study turn-based stochastic zero-sum games with lexicographic preferences over reachability and safety objectives. Stochastic games are standard models in control, verification, and synthesis of stochastic reactive systems that exhibit both randomness as well as angelic and demonic non-determinism. Lexicographic order allows to consider multiple objectives with a strict preference order over the satisfaction of the objectives. To the best of our knowledge, stochastic games with lexicographic objectives have not been studied before. We establish determinacy of such games and present strategy and computational complexity results. For strategy complexity, we show that lexicographically optimal strategies exist that are deterministic and memory is only required to remember the already satisfied and violated objectives. For a constant number of objectives, we show that the relevant decision problem is in NP∩coNP , matching the current known bound for single objectives; and in general the decision problem is PSPACE -hard and can be solved in NEXPTIME∩coNEXPTIME . We present an algorithm that computes the lexicographically optimal strategies via a reduction to computation of optimal strategies in a sequence of single-objectives games. We have implemented our algorithm and report experimental results on various case studies.
Publishing Year
Date Published
2020-07-14
Proceedings Title
International Conference on Computer Aided Verification
Volume
12225
Page
398-420
Conference
CAV: Computer Aided Verification
ISSN
eISSN
IST-REx-ID

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Chatterjee K, Katoen JP, Weininger M, Winkler T. Stochastic games with lexicographic reachability-safety objectives. In: International Conference on Computer Aided Verification. Vol 12225. Springer Nature; 2020:398-420. doi:10.1007/978-3-030-53291-8_21
Chatterjee, K., Katoen, J. P., Weininger, M., & Winkler, T. (2020). Stochastic games with lexicographic reachability-safety objectives. In International Conference on Computer Aided Verification (Vol. 12225, pp. 398–420). Springer Nature. https://doi.org/10.1007/978-3-030-53291-8_21
Chatterjee, Krishnendu, Joost P Katoen, Maximilian Weininger, and Tobias Winkler. “Stochastic Games with Lexicographic Reachability-Safety Objectives.” In International Conference on Computer Aided Verification, 12225:398–420. Springer Nature, 2020. https://doi.org/10.1007/978-3-030-53291-8_21.
K. Chatterjee, J. P. Katoen, M. Weininger, and T. Winkler, “Stochastic games with lexicographic reachability-safety objectives,” in International Conference on Computer Aided Verification, 2020, vol. 12225, pp. 398–420.
Chatterjee K, Katoen JP, Weininger M, Winkler T. 2020. Stochastic games with lexicographic reachability-safety objectives. International Conference on Computer Aided Verification. CAV: Computer Aided Verification, LNCS, vol. 12225. 398–420.
Chatterjee, Krishnendu, et al. “Stochastic Games with Lexicographic Reachability-Safety Objectives.” International Conference on Computer Aided Verification, vol. 12225, Springer Nature, 2020, pp. 398–420, doi:10.1007/978-3-030-53291-8_21.
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